کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898766 | 1631498 | 2018 | 27 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Nonlinear instability of half-solitons on star graphs
ترجمه فارسی عنوان
ناپایداری غیرخطی نیم سولیتون بر روی نمودارهای ستاره
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
We consider a half-soliton stationary state of the nonlinear Schrödinger equation with the power nonlinearity on a star graph consisting of N edges and a single vertex. For the subcritical power nonlinearity, the half-soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative. By using normal forms, we prove that the degenerate critical point is a saddle point, for which the small perturbations to the half-soliton state grow slowly in time resulting in the nonlinear instability of the half-soliton state. The result holds for any Nâ¥3 and arbitrary subcritical power nonlinearity. It gives a precise dynamical characterization of the previous result of Adami et al. (2012) [2], where the half-soliton state was shown to be a saddle point of the action functional under the mass constraint for N=3 and for cubic nonlinearity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 264, Issue 12, 15 June 2018, Pages 7357-7383
Journal: Journal of Differential Equations - Volume 264, Issue 12, 15 June 2018, Pages 7357-7383
نویسندگان
Adilbek Kairzhan, Dmitry E. Pelinovsky,